Which preposition to use with perimeter

of Occurrences 9%

To enlarge the perimeter of defence would be to increase the difficulties and require a much larger force than was available, and there was no intention of going beyond Foka before the main operation against Jerusalem was started.

as Occurrences 1%

In wagon boilers the proportion of the perimeter of the flue which is effective as heating surface, is to the total perimeter as 1 to 3, or, in some cases as 1 to 2.5; and with any given area of flue, therefore, the length of the flue must be from 3 to 2.5 times greater than would be necessary if the total surface were effective, else the requisite quantity of heating surface will not be obtained.

by Occurrences 1%

Q.Will this proportion alter if the form of the flue be changed? A.It is clear, that with any given area of flue, to increase the perimeter by adopting a different shape is tantamount to a diminution of the length of the flue; and, if the perimeter be diminished, the length of the flue must at the same time be increased, else it will be impossible to obtain the necessary amount of heating surface.

Which preposition to use with  perimeter